A small-sample nonparametric independence test for the Archimedean family of bivariate copulas

Abstract

In this paper we study the problem of independence of two continuous random variables using the fact that there exists a unique copula that characterizes independence, and that such copula is of Archimedean type. We use properties of the empirical diagonal to build nonparametric independence tests for small samples, under the assumption that the underlying copula belongs to the Archimedean family, giving solution to an open problem proposed by Alsina et al. [2]. © 2008 Springer-Verlag Berlin Heidelberg.